Daniel is 40 years older than William. Nineteen years ago, Daniel was 5 times as old as William. How old is William now?
Explanation: We can use the given information to write down two equations that describe the ages of Daniel and William. Let Daniel's current age be $d$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $d = w + 40$ Nineteen years ago, Daniel was $d - 19$ years old, and William was $w - 19$ years old. The information in the second sentence can be expressed in the following equation: $d - 19 = 5(w - 19)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $w$ , it might be easiest to use our first equation for $d$ and substitute it into our second equation. Our first equation is: $d = w + 40$ . Substituting this into our second equation, we get the equation: $(w + 40)$ $-$ $19 = 5(w - 19)$ which combines the information about $w$ from both of our original equations. Simplifying both sides of this equation, we get: $w + 21 = 5 w - 95$ Solving for $w$ , we get: $4 w = 116$ $w = 29$.